2. Integrate: a) Sx cos(x²) dx g) [3 cos(2nx) dx b) S tan³ x sec²x dx h) Se2% sin(e²*) dx c) S cot x dx d) S sin’ x cos x dx e) S tan² x dx (use a Pythagorean Id.) f) S(x – 1) cos(x² – 2x) dx

Q: Integrate S(cos x)e*+sin xdx B. et-sinx + C A. -e4+sin x + C c. e4+sinx + C D. e-4+sinx +C A В C D

A: Given: I=∫cosxe4+sinxdx  ....(1)   We know that; ∫eax+bdx=1aeax+b+C

Q: S(csc x cot x + 9x°)dx Csc x + x° +c - sec x + x³ +c | CSc x + x9 - sin x + x³ +c sec x + r9 + c

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Q: Activity 3: 1. ſx²dx 2. SVx?dx 3. S(x³+x²)dx 4. SVx*dx 5. fx-2dx 6. S tan?x dx 7. S(1 – cos u)du 8.…

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Q: e (a) S sin* x dx

A: Apply reduction formula:∫sinnx dx = n-1n∫sinn-2(x)dx - cosx. sinn-1(x)nwith n=4∫sin4x dx =…

Q: Evaluate Se²x 2x Se²x 2x cos (5x) dx. cos (5x) dx = e2x. (5 sin (5x) + 2 cos (5x)) 19 + C

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Q: V. Show that: 1. [(cosx-sin x)'dx = x+ cos 2x +C 2.

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Q: fsin²7x dx Select one: O a. O b. O c. O d. O e. 7x - sin²7x cos 7x 14 7x sin7x cos 7x 7 7x + sin7x…

A: Formula used

Q: b) Solve to find if y = Tant VE and t = 4x-2 – secx dz b) if z = sin20, and 0 = [cos(w) + 1]² + cos…

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Q: a dx = 1+ sin(ax) Select one: a. tan(ax) – sec(az) + C b. ax + In | csc(az) – cot(az)| + C c. In |1+…

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Q: x-1 c) Let f (x) = x+ 0. Find by using numerical calculations in a tabular x2 - 1 which x approached…

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Q: 1. A. f sin 2x cos 5x dx B. f cos 2x cos 3x dx c. ftan³x sec5x dx

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Q: Evaluate: y +y = - cos X COSX A. y = 0, sinx + Ca cosx + x sin x 8. C, COSX + Ca casx t x cas X C. y…

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Q: 1. Determine (i) |cos (2x– 7) dx dx (ii) x +9 (ii) dx 4-9x² 2. Determine (sin x cos x dx using (1)…

A: Since, you have posted multiple questions we will only first question with three subparts as per our…

Q: -1 Let f(x) = (3 sin z + 4 cos z)tan f'(x) = %3D

A: Given  f(x)=(3sinx+4cosx)tan-1xTo find f'(x):

Q: Q3) A: Find y if: a- y = sin 2x + 2 cos x c- y = sin √x (As... b- y = secx. csc x d- y = tan(2x + 1)

A: Please see the attachment

Q: a) Use suitable sum and difference identities for hyperbolic functions to show that sinh(5x)…

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Q: 3. Show that: • T/2 sin" x dx • T/2 cos" x dx

A: Recall the property of definite integral:

Q: 4. Find d?y/dx² for the following functions: a) y = sin x? cos 2x b) y = cos (sec2 3x) c) y = x²(x³…

A: Since you have asked multiple questions, we are answering the first question for you as of now. If…

Q: : (a) Evaluate S cosx sinx V1 – sin+x_dx. (b) Evaluate S V1 – x² dx.

A:

Q: M tan? x dx

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 3n 2n TE S. (sin x + cos y)e dx dy dz A. 2n(e2n + e3) B. 2m(e2 – e3") c. 2m(e + e2") p. 2n(e- e")

A: For the solution follow the next steps.

Q: (d) ſ tan² 3t dt 5 cos? x – 3 tan x dx - (e) S cOs X

A: The integration of the integrals is d) tan2(3t)  e) (5cos2x-3tanx) /cosx